Standard Form

Standard Form: The Vertex

Then, take the x-value and substitute it back into the equation to find the y.

Standard Form: The Vertex

Find the y-coordinate:

x = -b / 2a

x = -(4) / 2(2)

x = -1

Find the x-coordinate:

a = 2

b = 4

c = -6

Vertex: (-1, -8)

Vertex Form

• a is always at the beginning, before any ( ) or x. If you don't see it, it's 1!

• h is always in ( ) with x. If you don't see it, it's 0!

• k is always at the end. If you don't see it, it's 0!

Vertex Form: The Vertex

Vertex: (h, k)

h is a liar! Take the OPPOSITE of the value you see in the equation.

k is trustworthy. You don't have to change the sign of k.

Vertex Form: The Vertex

a = 1, h = 1, k = 0

Vertex: (1, 0)

y = (x - 1)²

a = 2, h = -3, k = -6

Vertex: (-3, -6)

y = 2(x + 3)² - 6

(Don't forget to change the sign of h from what you see in your equation!)

Plotting Points

Use the a-value to help you!

After you plot your vertex on the graph, the adjacent (directly beside) points are determined by the a-value.

Move over one square to the right, then go up or down a number of squares that's equal to the a-value. Then, do the same moving to the left.

(If a is positive, move up, and if a is negative, move down.)

Start at the vertex.
Go right 1 and down 2, then plot a point.
Then, go back to the vertex and go left 1 and down 2, then plot a point.

If a = -2:

Start at the vertex.
Go right 1 and up 1, then plot a point.
Then, go back to the vertex and go left 1 and up 1, then plot a point.

If a = 1:

Plotting Points (Examples)